| Summary: | M.Ed. === Our world is becoming more mathematical. We are constantly surrounded by mathematical situations and are regularly required to make mathematical decisions. These decisions require number sense, estimation skills, ability to analyse data intelligently, knowledge of two and three-dimensional geometry and many other abilities not often taught in school. Halpern (1992:1) states: "...as a nation we not only need competent scientists and engineers, we also need a citizenry that is literate in mathematics issues." Reyes and Stannic (1998:26) support this view as they state: "Knowledge of mathematics is essential for all members of our society. To participate in our democratic processes and to be unrestricted in career choice and advancement, people must be able to apply mathematical ideas." Learners leaving school need to be able to use available technology and to reason mathematically, be confident of their abilities, be able to communicate mathematically and be problem solvers. The introduction of technology into the lives of many people has called upon their background of mathematics to cope with mathematical problems and manipulating technological instruments. The relationship between mathematics and technology is emphasised by Dowling and Noss (1990:24) when they say: "New technology is a powerful tool which opens up new areas of mathematics and changes the way in which society makes use of mathematics in the factory, office and home". The Cockcroft Committee (1982), in their report on an inquiry into the teaching of Mathematics in schools, sees the main task of mathematics teachers as: "Enabling each learner to develop within his own capabilities the mathematical understanding and skills required for adult life, for employment and further study". The most important contribution for the purpose of this study, was the emphasis placed on cognitive aims to equip learners with numerical understanding and skills. Other contributions were to develop logical thinking and to expand their ability to look for patterns and explain them and to develop an awareness of the link between mathematics and everyday situations. This report (1982) motivated the researcher to review how teachers are teaching. This means that there will be an investigation into how children learn mathematics and not just what should be taught. Naidoo, Smit and Van Heerden (1995:7) also emphasise this by stating that "...the advance in technology at this time changed educational thinking more, making it even more important to further investigate how children actually learn." Yildirim (1994:28) argues that "... improving student's thinking ability is accepted as an important goal of education, and schools are considered places where thinking skills can be promoted. However, ways in which this should be done is a matter of controversy among educators." He further postulates that the best way to improve student thinking involves deep and thoughtful subject matter instruction in which students are encouraged to think reflectively rather than to merely cite the facts. The central characteristics of mathematical thinking are the determination of relationship and their application. It includes the ability to analyse a given situation or experience; to distinguish between applicable data and those which are not applicable; to classify and arrange these data; to abstract relationships from them, and finally to symbolize them for future use and application in new situations. Therefore it is important and essential for students to be taught how to approach the problems. This is one way of encouraging inquisitive and creative mathematics. Well-developed thinking skills are useful in almost every life situation, therefore there is a need to design instructional programmes that focus on the acquisition and uses thinking skills that are needed to find and solve mathematical problems.
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